I
Hydrophysical and Ecological Models of Shallow Lakes
and Reservoirs
; Summary Report of an I l A S A Workshop
I
April 11 -14,1978
:
!
Sven E. Jdrgenson, Editor
CP-78-14
OCTOBER 1979
HYDROPHY SICAL AND ECOLOGICAL MODELS OF SHALLOW LAKES AND RESERVOIRS Summary Report of an IIASA Workshop April 1 1-14, 1978
Sven E. Jdrgensen, Editor
The Royal Danish School o f Pharmacy Copenhagen, Denmark
CP-78-14 October 1979
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS
. Laxenburg, Austria
Views e x p r e s s e d h e r e i n a r e t h o s e o f t h e c o n t r i b u t o r s and n o t n e c e s s a r i l y t h o s e o f t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s .
C o p y r i g h t 0 1 9 7 9
I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d Systems A n a l y s i s
A l l r i g h t s r e s e r v e d . No p a r t o f t h i s p u b l i c a t i o n may b e r e p r o - d u c e d o r t r a n s m i t t e d i n a n y form o r by a n y means, e l e c t r o n i c o r m e c h a n i c a l , i n c l u d i n g p h o t o c o p y , r e c o r d i n g , o r a n y i n f o r m a t i o n s t o r a g e o r r e t r i e v a l s y s t e m , w i t h o u t p e r m i s s i o n i n w r i t i n g from t h e p u b l i s h e r .
PREFACE
An i m p o r t a n t s u b t a s k w i t h i n t h e R e s o u r c e s a n d E n v i r o n m e n t A r e a (REN) o f t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s (IIASA) i s t h e d e v e l o p m e n t a n d a p p l i c a t i o n o f m o d e l s f o r e n v i r o n m e n t a l q u a l i t y c o n t r o l a n d management. The i n i t i a l o b j e c - t i v e s o f t h i s t a s k a r e t o a s s e s s e x i s t i n g m o d e l s , t o d e v e l o p i m - p r o v e d h y d r o p h y s i c a l a n d e c o l o g i c a l m o d e l s a s t o o l s f o r t h e a n a l - y s i s o f w a t e r q u a l i t y p r o b l e m s , a n d t o a p p l y t h e s e m o d e l s t o l a k e s , r e s e r v o i r s , a n d r i v e r s y s t e m s .
On S e p t e m b e r 13-16, 1 9 7 7 , a w o r k s h o p o n t h e g e n e r a l a s p e c t s o f w a t e r q u a l i t y m o d e l i n g (IIASA CP-78-10) was h e l d a t IIASA.
The m o s t r e c e n t t h e o r e t i c a l d e v e l o p m e n t s i n t h e f i e l d o f W a t e r Q u a l i t y w e r e d i s c u s s e d a t t h i s m e e t i n g . A t t h e same t i m e t h e a p p l i c a t i o n o f h y d r o p h y s i c a l a n d e c o l o g i c a l m o d e l s t o v a r i o u s w a t e r b o d i e s was c o n s i d e r e d . As a r e s u l t o f t h i s w o r k s h o p i t was d e c i d e d t h a t a t t e n t i o n s h o u l d b e f o c u s s e d o n t h e w a t e r q u a l - i t y p r o b l e m s o f n a t u r a l l a k e s a n d man-made impoundments (reser- v o i r s ) . I n a d d i t i o n , i t was f e l t t h a t IIASA c o u l d make a n i m p o r - t a n t c o n t r i b u t i o n t o t h e u s e o f m o d e l s f o r w a t e r q u a l i t y c o n t r o l a n d management p u r p o s e s by a t t e m p t i n g t o b r i d g e t h e g a p b e t w e e n t h e h y d r o p h y s i c a l and e c o l o g i c a l m o d e l i n g d i s c i p l i n e s . A c c o r d - i n g l y , i t was d e c i d e d t o c o n v e n e two s p e c i a l i z e d w o r k s h o p s . The f l r s t o f t h e s e was o n H y d r o p h y s i c a l a n d E c o l o g i c a l P l o d e l l i n g o f Deep L a k e s a n d R e s e r v o i r s (IIASA CP-78-7) h e l d o n December 1 2 - 1 5 , 1 9 7 7 , i n L a x e n b u r g . The s e c o n d o f t h e s e was o n h y d r o l o g i c a l a n d e c o l o g i c a l m o d e l i n g o f s h a l l o w l a k e s a n d r e s e r v o i r s , a n d was h e l d
o n A p r i l 11-14, 1 9 7 8 , i n L a x e n b u r g .
The s u b j e c t o f d e e p l a k e s a n d r e s e r v o i r s c h o s e n f o r t h e December w o r k s h o p i m p l i e s a b a s i c c o n c e r n w i t h s t r a t i f i c a t i o n a n d i n t e r a c t i o n s a t t h e f r e e s u r f a c e b o u n d a r y r a t h e r t h a n w i t h c o n d i t i o n s o f f u l l v e r t i c a l m i x i n g a n d b o t t o m s e d i m e n t i n t e r - a c t i o n s .
The subject of shallow lakes and reservoirs chosen for the April workshop implies a basic concern with the condition of full vertical mixing and bottom sediment interactions. This report summarizes the results of this second workshop, which was attended by 28 people representing 14 countries and by 13 IIASA staff mem- bers from
5
countries. Prior to the workshop, a set of questions related to ecological and hydrophysical modeling problems were formulated by the IIASA staff and sent to the participants with the request to indicate on which questions they would like to give a short presentation as a start to the discussion of the questions. Topics discussed at the workshop included:- -
C h a r a c t e r i s t i c F e a t u r e s o f S h a l l o w L a k e s a n d R e s e r v o i r s : influence of wind and wave action, longitudinal and ver- tical mass transport processes, exchange of nutrients between the water body and the sediments, influence of sediment types on the transformation processes of chem- ical compounds- -
H y d r o p h y s i c a l M o d e l s : horizontal and vertical transport and diffusion processes, interaction across the water/sediment interface
--
Eco l o g i c a l M o d e l s : evaluation of available data by simple models, sensitivity analysis, improvement in the quantity of data, further development of ecological models of shallow lakes taking into account the binding and mobilization of nutrients in the sediments- -
W a t e r Q u a l i t y M o d e l s : limiting nutrients/carbon, nitro- gen, phosphorus, element-cycle models/simple and complex models--
F i e l d D a t a C o l l e c t i o n a n d Model V e r i f i c a t i o n T e c h n i q u e s : coordination of chemical and biological field measure- ments with water quality models, choice of parameters--
P o s s i b l e C a s e S t u d i e sThese discussions are summarized in the Introduction.
In addition, some of the participants presented original papers at the discussion of the ecological and hydrophysical questions. These papers are included in the second part of this Proceedings following the Discussion. It should be noted that a paper by H.A. Tsvetova on Numerical Modeling of the Dynamics of Lake Baikal was presented at the workshop. It is not included in these proceedings but will be published separately in IIASA's Professional Paper Series. The paper was originally intended for presentation at the workshop on Hydrophysical and Ecological Modelling of Deep Lakes and Reservoirs.
This workshop was an excellent opportunity for experienced modelers from both the ecological and hydrophysical areas to come together for a discussion of problems of mutual interest and to exchange ideas and viewpoints.
Oleg F. Vasiliev Leader
,
Resources andEnvironment Area
International Institute for Applied Systems Analysis
Sven E. J4rgensen Royal Danish School
of Pharmacy
ACKNOWLEDGMENTS
The e d i t o r would l i k e t o e x p r e s s h i s t h a n k s t o a l l t h o s e who c o n t r i b u t e d t o t h e workshop on Hydrophysical and E c o l o g i c a l Models of Shallow Lakes and R e s e r v o i r s , whether by f o r m a l p r e s e n - t a t i o n s o r t h r o u g h p a r t i c i p a t i o n i n t h e d i s c u s s i o n s . S p e c i a l t h a n k s a r e due t o t h e p a r t i c i p a n t s who a c t e d a s g e n e r a l r e p o r t e r s and p r e p a r e d w r i t t e n summaries. The e d i t o r a c c e p t s f u l l r e s p o n - s i b i l i t y f o r e r r o r s o r o m i s s i o n s .
CONTENTS
INTRODUCTION S . E. J b r g e n s e n
PART I DISCUSSION
D i s c u s s i o n o f Q u e s t i o n s R e l a t e d t o H y d r o p h y s i c a l a n d Eco- l o g i c a l Modeling o f S h a l l o w Lakes a n d R e s e r v o i r s
PART I1 PAPERS PRESENTED AT THE CONFERENCE
The Role o f I r o n and Calcium i n t h e C y c l i n g o f P h o s p h a t e s i n S h a l l o w Lakes
L . L i j k Z e m a a n d A . H . M . H i e Z t j e s
The P r e d i c t i o n o f S o l u t i o n s t o Management and E n g i n e e i n g Problems R e l a t e d t o t h e E u t r o p h i c a t i o n o f Water B o d i e s V . A . V a v i Z i n , V . B . V a s i Z y e v , M . Y u . T s i t k i n , a n d
S . V . B a g o t s k i i
Two Examples o f t h e Use o f Hydrodynamic Models i n Eco- l o g i c a l S t u d i e s
J . F . Pauz
The Modeling o f A q u a t i c Ecosystems o f S h a l l o w Lakes Ex- c h a n g i n g M a t t e r w i t h t h e S e d i m e n t a n d w i t h N e i g h b o r i n g Water B o d i e s
P. M a u e r s b e r g e r
Development and V e r i f i c a t i o n o f a Model f o r P r e d i c t i n g E u t r o p h i c a t i o n T r e n d s i n C z e c h o s l o v a k i a
M . ~ t r a g k r a b a
The M o d e l i n g o f N u t r i e n t Exchange b e t w e e n S e d i m e n t a n d 9 7 W a t e r
G. ~ o Z i i n k a i
S i m u l a t i o n Model o f a n O l i g o t r o p h i c Lake J.M. S v i r e z h e v , N . K . L u c k y a n o v , D . O . L o g o f e t E v a l u a t i o n o f A v a i l a b l e P h o s p h o r u s Models M . W. L o r e n z e n a n d F . M . H a y d o c k
T h e o r e t i c a l I n v e s t i g a t i o n s i n t o t h e Development o f a n 130 I n t e n s i v e l y Used S h a l l o w Lake w i t h a R i v e r F l o w i n g i n t o
I t K . B a u e r
E u t r o p h i c a t i o n M o d e l i n g E f f o r t s f o r L a k e B a l a t o n P. C z i i k i , J . F i s c h e r , L . H a j d u , a n d G . ~ o Z i i n k a i U s e o f C h l o r o p h y l l / S e c c h i D i s c R e l a t i o n s h i p s M . E. L o r e n z e n
P a r t i c i p a n t s o f t h e Workshop on H y d r o p h y s i c a l and Eco- 154 l o g i c a l M o d e l i n g o f S h a l l o w L a k e s a n d R e s e r v o i r s ,
A p r i l 11-14, 1 9 7 8 .
INTRODUCTION S
. E.
JfbrgensenThere are many specialized models for solving eutrophication problems. They range from those in which one to four nutrients may be considered, to those in which one or several layers and segments may be considered. Some models are based on constant stoichiometry, others on independent nutrient cycles. Unfortu- nately most of the models have not been validated or calibrated.
No universal model exists for solving the above problems.
A particular model is selected on an individual basis according to the nature of the problem to be solved, and most models are based on biological/chemical knowledge of the processes taking place in the lake. A black box approach seems to be inappropriate for modeling a lake system, because it does not provide general information about the aquatic system; but experience indicates that a multidisciplinary scientific approach is required.
Many models are limited by the lack of suitable field data for model calibration and verification. Therefore, in the model, the description of an ecosystem is based upon the data, and thus an accurate description of the ecosystem is dependent upon the accuracy of the data (e.g., measurement error levels, sampling accuracy). These general items will be mentioned briefly in several of the questions listed in the agenda of this workshop.
What i s t h e s t a t e o f t h e a r t o f l a k e m o d e l i n g t o d a y ? Using a u n i v e r s a l model, i t i s i m p o s s i b l e t o f i n d an improved s c i e n t i f i c d e s c r i p t i o n o f a s p e c i f i c p r o c e s s i n a n a q u a t i c e c o s y s t e m , b u t i t i s p o s s i b l e t o o b t a i n an improved d e s c r i p t i o n o f a s p e c i f i c p r o - c e s s by u s i n g a submodel b a s e d on i n t e n s i v e i n s i t u m e a s u r e m e n t s , o r by e x a m i n i n g a n i n d i v i d u a l b i o l o g i c a l / c h e m i c a l p r o c e s s i n t h e l a b o r a t o r y . T h i s d o e s n o t mean t h a t u n i v e r s a l models a r e n o t u s e f u l - - t h e y c a n be u s e d t o examine t h e o v e r a l l b e h a v i o r o f s e v - e r a l i n t e r a c t i n g p r o c e s s e s , and may t h e r e f o r e b e n e c e s s a r y f o r management p u r p o s e s .
Submodels, however, a r e more u s e f u l a s a s c i e n t i f i c t o o l . The s e l e c t i o n o f an a p p r o p r i a t e model i s d e p e n d e n t upon f i n d i n g t h e c o r r e c t b a l a n c e o f i n f o r m a t i o n , f o r e x a m p l e , a l l i m p o r t a n t p r o c e s s e s must b e i n c l u d e d , b u t n o t e v e r y d e t a i l o f l e s s impor- t a n t p r o c e s s e s . I f t o o many s t a t e v a r i a b l e s a r e i n c l u d e d t h e model w i l l b e u n w i e l d y , and i f t o o many p a r a m e t e r v a l u e s a r e
i n t r o d u c e d , t h i s c o u l d l e a d t o i n a c c u r a c i e s . B u t , i n c o n t r a s t , a model t h a t i s t o o s i m p l e m i g h t n o t d e s c r i b e a d e q u a t e l y t h e dynamics o f t h e s y s t e m .
No g e n e r a l p r i n c i p l e s u n d e r l y i n g t h e r e a c t i o n s o f e c o s y s t e m s h a v e b e e n f o r m u l a t e d , and a more r e d u c t i o n i s t a p p r o a c h t o m o d e l i n g d o e s n o t seem t o b e f e a s i b l e . I n s t e a d a h o l i s t i c a p p r o a c h em- b o d y i n g a s e t o f e c o l o g i c a l p r i n c i p l e s i s n e e d e d . The d e s c r i p t i o n o f c u r r e n t e c o l o g i c a l s y s t e m s c a n b e compared t o t h a t o f g a s e s i n a room, by means o f v e l o c i t y , d i r e c t i o n , and g r o u p s o f mole- c u l e s . I n t h e f u t u r e , e c o l o g i c a l s y s t e m s w i l l b e e x p r e s s e d by g e n e r a l l a w s a n a l o g o u s t o t h o s e o f g a s e s , and w i l l c o n t a i n t e r m s e q u i v a l e n t t o A v o g a d r o ' s number and t h e l i k e . These and o t h e r f u n d a m e n t a l p r o b l e m s o f c u r r e n t w a t e r q u a l i t y m o d e l i n g w i l l b e d i s c u s s e d i n t h e c o u r s e o f t h e s e Workshop P r o c e e d i n g s .
Part I DISCUSSION
DISCUSSION OF QUESTIONS RELATED TO HYDROPHYSICAL AND ECOLOGICAL MODELING OF SHALLOW LAKES AND RESERVOIRS
A. ECOLOGICAL TOPICS
1 . The v a l i d i t y o f c o n s t a n t s t o i c h i o m e t r i c m o d e l s v e r s u s e l e m e n t - c y c l e m o d e l s . How many e l e m e n t c y c l e s a r e n e c e s s a r y f o r a e u t r o - p h i c a t i o n m o d e l ?
Reported by G. van Straten
In general a preference was shown for element-cycle models or at least for variable stoichiometric models, in order to pre- dict algal bloom. This is because each of the nutrients--phos- phorus, nitrogen, and silica--is to some extent cycled indepen- dently, owing to such phenomena as luxury uptake. The use of an element-cycle type of model would seem to be essential in the following two instances:
--
If a switch occurs during the season, whereby the limiting factor passes from one nutrient to another (e.g., luxury phosphorus uptake, when silica is the limiting nutrient)--
If the internal nutrient cycle is significant in compar- ison with the external loading (internal cycling in most cases is more important for shallow lakes than for deep lakes)I n a d d i t i o n , t h e q u e s t i o n was r a i s e d w h e t h e r t h e p h o s p h o r u s / n i t r o g e n r a t i o i n t h e c e l l had some i n f l u e n c e o n t h e s e t t l i n g r a t e . I f t h i s i s t h e c a s e , t h e n a c o n s t a n t s t o i c h i o m e t r i c model c a n n o t b e u s e d . I n some c a s e s o n l y a n i n d e p e n d e n t e l e m e n t - c y c l e m o d e l i s a b l e t o p r e d i c t a c c u r a t e l y t h e t i m e o r t h e p e a k h e i g h t o f a n a l g a l bloom maximum. However, some s i m u l a t i o n r e s u l t s s h o w i n g o n l y a m i n o r d i f f e r e n c e b e t w e e n t h e two t y p e s o f m o d e l s h a v e b e e n r e p o r t e d . T h i s m i n o r d i f f e r e n c e i s more a p p a r e n t i f bhe c h a n g e s i n p h y t o p l a n k t o n c o n c e n t r a t i o n s a r e s m a l l . A s e r i o u s d i s a d v a n t a g e o f t h e i n d e p e n d e n t e l e m e n t - c y c l e model i s t h a t it r e q u i r e s t h e i n t r o d u c t i o n o f more p a r a m e t e r s i n t o t h e model.
T h e r e f o r e i n c e r t a i n c a s e s i t may b e b e n e f i c i a l t o u s e a c o n s t a n t s t o i c h i o m e t r i c model t o g e t h e r w i t h m e a s u r e d v a l u e s f o r t h e b i o m a s s / n u t r i e n t r a t i o . The b e s t e x a m p l e o f t h i s i s i n t h e d e s i g n o f a n a l g a l g r o w t h b a s i n t o b e o p e r a t e d u n d e r s t e a d y c o n d i t i o n s .
However, many o f t h e p a r a m e t e r s i n t h e i n d e p e n d e n t e l e m e n t - c y c l e m o d e l s a r e w e l l known, s u c h a s t h e minimum a n d maximum c o n c e n t r a t i o n o f p h o s p h o r u s , n i t r o g e n , c a r b o n , a n d s i l i c a . C a l i - b r a t i o n c a n t h u s b e c a r r i e d o u t f o r r e s t r i c t e d p a r a m e t e r i n t e r v a l s , c o u n t e r b a l a n c i n g t h e d i s a d v a n t a g e o f h a v i n g more p a r a m e t e r s i n t h e m o d e l .
The c o n c l u s i o n o f t h i s d i s c u s s i o n i s t h a t c o n s t a n t s t o i c h i o - m e t r i c m o d e l s may b e u s e d t o o b t a i n a r e a s o n a b l e a p p r o x i m a t i o n o f t h e t i m e o r p e a k h e i g h t o f a l g a l bloom, p r o v i d i n g t h a t n o g r e a t c h a n g e s i n i n t e r c e l l u l a r b i o m a s s n u t r i e n t r a t i o a r e t o b e e x p e c t e d . B u t a d e t a i l e d a n d more a c c u r a t e d e s c r i p t i o n c a n o n l y b e o b t a i n e d f r o m a n u t r i e n t - c y c l e t y p e o f model a t t h e e x p e n s e o f i n t r o d u c i n g more p a r a m e t e r s , m o s t o f w h i c h a r e a p p r o x i m a t e l y known, b u t r e q u i r e a c c u r a t e e s t i m a t i o n .
2 . W h i c h e q u a t i o n s a r e m o s t s u i t a b l e f o r d e s c r i b i n g t h e n u t r i e n t u p t a k e r a t e s by p h y t o p l a n k t o n o f ( a ) p h o s p h o r u s , ( b l n i t r o g e n
( N H :
,
N O ; a s w e l l a s N O ; ) , ( c ) c a r b o n , ( d ) s i l i c a ? How s h o u l d t h e g r o w t h and m o r t a l i t y o f p h y t o p l a n k t o n w i t h s i n g l e and m u l t i p l e c e l l u l a r c o n c e n t r a t i o n o f n u t r i e n t s be m o d e l e d ? Which l i g h t and t e m p e r a t u r e e x p r e s s i o n s a r e s u i t a b l e ?R e p o r t e d by M.W. L o r e n z e n
Equations (1 )
,
(2),
and (3) for nutrient uptake in phyto- plankton growth were presented:growth = ymax f (T)
.
f (PA).
f (NA).
f (CA) f (A),
(1 )where A refers to algal concentration, and T, P, N, and C are temperature, phosphorus, nitrogen, and carbon. The nutrient uptake--e.g., for phosphorus--can be described by Equation (2).
'Amax PHYT
-
PAUP = UP P
s
max PAmax PHYT
-
PAmin PHYT PHYT Kp + pS Iwhere S represents dissolved nutrient.
A
differentiation between ammonia and nitrate uptake was included by the use of Equation (3) :UN (Nit) = UNmin (Nit)
+
(1- )
N m a X N i t-
UNmin (Nit ) ).
The effect of temperature was presented as the functional rela- tionship shown in Figure 1. For this type of function it is recommended that a look-up table is employed in order to minimize computer time.
Figure 1. Phytoplankton growth, f (T), as a function of temperature, T.
It is recommended that these expressions should be used in situations discussed in conjunction with question Al. The
Michaelis-Menten expression, which is often used, shows, however, little difference from the more detailed description referred to above when bhort-term batch culture experiments are interpreted.
It has been suggested that regression analysis can be used to lump together unknown parameter values when long-term data are available. This method can only be recommended for simple cases.
It was also stated that when combining a number of limiting terms (nitrogen, phosphorus, temperature, light, silica) a minimum or threshold approach is superior to a multiplicative equation, see above.
However, the whole process of nutrient uptake and growth is more complex and difficult; it seems necessary to assume that parameters change with the temperature. The same is true for the "Michaelis-Menten constants", since they change with light intensity. Unfortunately, there are at present insufficient data to construct a response function for phytoplankton growth as a function of temperature, nitrogen, phosphorus, silica, etc. A schematic presentation of the values of the various rate-limiting terms throughout an annual cycle might clarify their relative importance at different times of the year. The question "How do we take the adaptation of phytoplankton into account?" merits
further discussion.
3 . Which e q u a t i o n i s r e l e v a n t f o r d e s c r i b i n g t h e g r a z i n g r a t e ? S h o u l d more t h a n o n e s p e c i e s o f z o o p l a n k t o n b e i n c l u d e d ?
Reported by D.O. Logofet
There are several types of predator-function responses to an increasing prey density; these include the prey/predator system of phytoplankton/zooplankton of particular interest here.
It is possible to select a model type by means of statistical procedures of hypothesis testing. In the simplest case of dis- tinguishing between two analytical expressions, f, and f2, the dichotomy problem takes the following form:
the hypotheses
H Iand
H2being
However, in complex simulation models with more than one state variable for both the phytoplankton and zooplankton species, the results often appear to be insensitive to variations of the grazing-rate parameters. From a theoretical point of view this insensitivity is caused by the data being insufficient to allow for a distinction to be made between two or more hypotheses. From an ecological point of view it is worth while to investigate the means to incorporate into the model a few varieties of phyto- plankton and at least two varieties of zooplankton. But for man- agement purposes often only an average situation is of interest, and in this case the modified Michaelis-Menten expression might suffice. In this expression, however, the influence of tempera- ture and the threshold effect of low phytoplankton concentration must be included.
4 . S h o u Z d s t a t e v a r i a b Z e s f o r f i s h a n d b e n t h o s b e i n c l u d e d i n a e u t r o p h i c a t i o n m o d e l ? How?
Reported by
P.Mauersberger
Theoretical considerations as well as recent limnological observations suggest that mass balances for fish populations
should be included in a eutrophication model. It was, for example, observed in a 60-hectare reservoir in Czechoslovakia that the
algal concentration was significantly reduced by a controlled low stock of predatory fish. This may even be used as a management tool in situations where it is impossible, or too expensive, to reduce the input of the limiting nutrient.
The effects of fish can sometimes be simulated in the eutro-
phication model simply by modifying the mortality coefficient in
the zooplankton equation. But for a more detailed model it appears
necessary to include fish explicitly as an additional state vari-
able. In this case the balance equation(s) for the fish
c o m p o n e n t ( s ) may b e s i m i l a r t o t h o s e f o r o t h e r c o n s u m e r g r o u p s . W h i l e t h e b i o m a s s f o r t h e f i s h c o m p o n e n t ( s ) may b e h i g h , <he e n e r g y o r mass f l u x e s b e t w e e n t h e h i g h e r t r o p h i c l e v e l s a r e s m a l l . I t may b e r e a s o n a b l e t o d i s t i n g u i s h i n some i n s t a n c e s b e t w e e n j u v e n i l e a n d a d u l t p a r t s o f t h e f i s h p o p u l a t i o n a n d t o t a k e t i m e v a r i a t i o n s i n t o c o n s i d e r a t i o n . O f c o u r s e , i t i s n o t e a s y t o g e t t h e b a s i c i n f o r m a t i o n a b o u t f i s h b i o m a s s , which i s r e q u i r e d when f i s h a r e i n c l u d e d a s a s t a t e v a r i a b l e i n a e u t r o - p h i c a t i o n model.
The c o m p l e t e model o f a s h a l l o w l a k e m u s t i n m o s t c a s e s i n c l u d e b e n t h i c c o m p o n e n t s , a n d a l s o e x c h a n g e p r o c e s s e s b e t w e e n s e d i m e n t a n d t h e w a t e r body, i n o r d e r t o o b t a i n t h e c o r r e c t n u t r i - e n t b a l a n c e s . I n many e u t r o p h i c l a k e s t h e p r i m a r y p r o d u c t i o n by t h e p h y t o b e n t h o s i s s m a l l i n c o m p a r i s o n w i t h t h e p r i m a r y p r o d u c - t i o n by t h e p h y t o p l a n k t o n . T h e r e f o r e , w e c a n assume t h a t o n l y t h e u p p e r n o n s h a d e d p a r t s o f t h e submerged p l a n t s a s s i m i l a t e n u t r i e n t s . Thus t h e g r o w t h o f p h y t o b e n t h o s d o e s n o t d e p e n d upon t h e i r b i o m a s s , b u t upon t h e o p t i c a l p r o p e r t i e s o f t h e o v e r l y i n g w a t e r body. Some o b s e r v a t i o n s s u g g e s t t h a t t h e d e c r e a s e o f p h y t o - b e n t h o s i n e u t r o p h i c l a k e s i s combined w i t h a n i n c r e a s e 6 f p h y t o - p l a n k t o n .
5. How s h o u l d n u t r i e n t e x c h a n g e b e t w e e n s e d i m e n t and w a t e r b e m o d e l e d ? How much d e t a i l w o u l d be n e e d e d i n t h e d e s c r i p t i o n o f b i o l o g i c a l , c h e m i c a l , and p h y s i c a l p r o c e s s e s t a k i n g p l a c e w i t h i n t h e b o t t o m s e d i m e n t ? S h o u l d t h e d e s c r i p t i o n b e d i f f e r e n t f o r a e r o b i c and a n a e r o b i c c o n d i t i o n s ?
R e p o r t e d by M.W. L o r e n z e n
The e x c h a n g e o f n u t r i e n t s b e t w e e n s e d i m e n t a n d w a t e r i s a k e y p r o c e s s i n t h e s i m u l a t i o n o f e u t r o p h i c a t i o n . U n f o r t u n a t e l y , a v a i l a b l e knowledge shows t h a t t h e r a t e o f e x c h a n g e v a r i e s con- s i d e r a b l y f r o m l a k e t o l a k e a n d i s a f u n c t i o n o f t i m e .
A model t h a t i n c l u d e s a " r e a c t i v e " s e d i m e n t l a y e r , o x i d i z e d a n d r e d u c e d c o n d i t i o n s , s o r b e d p h o s p h o r u s , c h e m i c a l l y f i x e d phos- p h o r u s , d i s s o l v e d p h o s p h o r u s i n i n t e r s t i t i a l w a t e r s , a n d i r o n compounds was p r e s e n t e d . The p r o c e s s e s c o n s i d e r e d i n t h i s model a r e s e d i m e n t a t i o n a n d d e c a y o f o r g a n i c m a t e r i a l ; d e s o r p t i o n ,
r e d u c t i o n , a n d o x i d a t i o n o f i r o n ; a d s o r p t i o n o f p h o s p h o r u s t o i r o n compounds; c h e m i c a l r e a c t i o n s a n d d i f f e r e n t r e d o x c o n d i t i o n s ; t r a n s p o r t b e t w e e n w a t e r a n d s e d i m e n t a n d t r a n s p o r t i n t o t h e d e e p e r s e d i m e n t s ; a n d oxygen t r a n s p o r t . A l l t h e r e a c t i o n s w e r e o f f i r s t o r d e r , a n d t h e a d s o r p t i o n f o l l o w e d L a n g m u i r ' s i s o t h e r m .
I n g e n e r a l i t was a p p a r e n t t h a t s e d i m e n t / w a t e r e x c h a n g e p r o - cesses s h o u l d b e c o n s i d e r e d i n more d e t a i l . However, t h e r e h a s n o t y e t b e e n s u f f i c i e n t f i e l d e x p e r i e n c e t o d e t e r m i n e t h e m o s t a p p r o p r i a t e f o r m u l a t i o n s .
6 . I n t h e e x c h a n g e p r o c e s s d e s c r i p t i o n , w h i c h p a r a m e t e r s a r e g e n e r a l , and w h i c h a r e s p e c i f i c ? I s i t p o s s i b l e t o e s t a b l i s h a r e l a t i o n s h i p b e t w e e n t h e s e p a r a m e t e r s and some s e d i m e n t c h a r a c t e r - i s t i c s ? How a r e l a b o r a t o r y e x p e r i m e n t s w i t h s u b s t r a c t e d ( d i s - t u r b e d o r u n d i s t u r b e d ) b o t t o m - s e d i m e n t s a m p l e s r e l e v a n t t o mod- e l i n g t h e e x c h a n g e o f n u t r i e n t s ?
R e p o r t e d by G. v a n S t r a t e n
From t h e d i s c u s s i o n i n c o n j u n c t i o n w i t h q u e s t i o n A5 i t i s c l e a r t h a t some b a s i c m o d e l s h a v e b e e n d e v e l o p e d f o r t h e s e d i m e n t s u b s y s t e m , b u t t h e y h a v e n o t y e t b e e n e x a m i n e d s u f f i c i e n t l y i n r e l a t i o n t o a v a i l a b l e d a t a . T h e r e f o r e , t h e a l t e r n a t i v e a p p r o a c h i s t o c o n d u c t l a b o r a t o r y e x p e r i m e n t s , p r e f e r a b l y w i t h u n d i s t u r b e d s e d i m e n t s a m p l e s . By v a r y i n g t h e pH a n d oxygen a n d n u t r i e n t con- t e n t i n t h e o v e r l y i n g w a t e r , i t s h o u l d b e p o s s i b l e t o p r o v i d e t h e i n f o r m a t i o n n e e d e d t o d e r i v e p a r a m e t e r s f o r a s c h e m a t i c s u b - m o d e l . An e x a m p l e o f s u c h a submodel was p r e s e n t e d . I n t h i s s u b - model o n l y i n t e r s t i t i a l p h o s p h o r u s a n d e x c h a n g e a b l e a n d nonex- c h a n g e a b l e f o r m s o f p h o s p h o r u s i n t h e s o l i d p h a s e a r e r e p r e s e n t e d . The n o n e x c h a n g e a b l e p o r t i o n i s d e t e r m i n e d f r o m t h e p h o s p h o r u s c o n t e n t i n o l d e r s e c t i o n s o f t h e s e d i m e n t , u s i n g t h e a r g u m e n t t h a t t h i s t y p e o f p h o s p h o r u s m u s t b e n o n e x c h a n g e a b l e , s i n c e it i s p r e s e n t i n t h e s e d i m e n t . S u c h a n a r g u m e n t i s q u e s t i o n a b l e , f o r i t i s known t h a t b i o t u r b a t i o n may b e r e s p o n s i b l e f o r m i x i n g t h e s e d i m e n t up t o a d e p t h o f 10-15 c e n t i m e t e r s .
The s u b m o d e l p r e s e n t e d g i v e s a n i n d i c a t i o n o f t h e p r o b l e m s t h a t may a r i s e f r o m s u c h a n e m p i r i c a l a p p r o a c h . S i n c e t h e simu- l a t i o n r e s u l t s o f t h e s u b m o d e l w e r e n o t s a t i s f a c t o r y , i t was
necessary to expand the model by adding other phosphorus components, thereby introducing more parameters. It may be concluded that
although empirical models are of value, the final solution can only come from a better understanding of the real chemical/
biological behavior of the sediment.
In the case of simultaneous diffusion and chemical reaction, which is a characteristic feature of undisturbed sediment layers, some insight may be obtained from a classical chemical engineering approach. The analysis of chemical engineering systems began in the 1950s. The enhancement of material flux toward or from the sediment due to reaction can be characterized by two dimension- less parameters, the Hatta number and the infinite enhancement rate, which can both be derived from measurable properties of the sediment. Such a theory explains the observed relationship of oxygen uptake rates according to the square root of the oxygen concentration in the overlying water. It also demonstrates the decrease in uptake or release rates as time proceeds, which may be of significance in the interpretation of laboratory experiments for parameter estimation.
7 . How c a n t h e s e t t l i n g o f p h y t o p l a n k t o n and d e t r i t u s be r e p r e - s e n t e d i n t h e m o d e l ?
Reported by
J.Fischer
Vertical transport results from a settling velocity of about 5-10 m/day and a vertical mixing. When considering the problem of a reduction in the amount of phytoplankton by diffusion, one has to suppose for the velocity that V
=f (Dl physical state), D
=diffusion coefficient, in order to avoid contradiction.
Some investigations in the Netherlands have shown that there is a better correlation between settling rate and light than
between settling rate and wind speed. It is probable that density gradients play an important role. Hypolimnion diffusion is much greater than epilimnion diffusion.
Since algae can change density, it might be necessary to
represent this factor in the model, in order to get an accurate
description of the settling rate. It is certain that the physio-
logical condition of the algae plays an important role in
determining this rate; typically the settling rate of the phyto- plankton is more rapid when their concentration is decreasing.
However, it is still uncertain whether such settling velocities have been measured realistically. Settling velocity does not appear to be a fundamental physical quantity, and there is little confidence in trap methods, although a rough estimate can be obtained by this kind of direct measurement.
8 . How do we m o d e l t h e f o l l o w i n g c h a i n o f p r o c e s s e s : o r g a n i c n i t r o g e n + ammonium + n i t r i t e + n i t r a t e ? A l s o how c a n s t a b l e d i s s o l v e d o r g a n i c n i t r o g e n s u c h a s humus b e m o d e l e d ?
Reported by L. Lijklema
Since phytoplankton bhow little preference for either ammonia or nitrate as a nutrient, it was considered unnecessary to give a detailed description of the nitrogen conversions. In most eco- logical models the process is represented as organic nitrogen +
ammonium + nitrite + nitrate, unless substantial oxygen consump- tion is involved in those conversion reactions. Also in many situations nitrate is the predominant nutrient in the water.
In chemostat experiments strongly fluctuating concentrations of nitrifying organisms may occur, but in the field such variations are generally slow. Therefore a temperature-dependent first- order conversion process for available nitrogen will be suffi- ciently accurate for most practical purposes.
9 . How d o we model t h e o r g a n i c + o r t h o - p h o s p h o r u s p r o c e s s ?
Reported by V.J. Bierman, Jr.
It was recognized that the transformation of phosphorus in the natural environment is the result of many complex and simul- taneous chemical and biological processes. The whole process can be simulated by using very detailed multicompartment kinetic models. In practice, the choice of the approach will depend on the particular objectives and the available data. Table 1 includes a representative sample of various approaches that have been pro- posed for modeling phosphorus transformations.
Table 1 . Some approaches t o t h e modeling of phosphorus t r a n s f o r m a t i o n s . a
schemes
DOP- DIP
---BOD-O2 DEFICIT
-
\10 DIP-DOP
Authors
S k o p i n t s e v ( 19 3 8 ) Plaksimova ( 1 9 7 2 )
G r i l l and Richards ( 1 9 6 4 ) Watt and Hayes ( 1 9 6 3 ) Corner ( 1 9 7 3 )
B a r s d a t e e t a l . ( 1 9 7 4 ) P o r t e r e t a l . ( 1 9 7 5 )
Richey e t a l . ( 1 9 7 5 )
Richey ( 1 9 7 7 )
Thomann e t a l . ( 1 9 7 3 )
~ i j z a t u l l i n and Leonov ( 1 9 7 5 )
%OP, D I P
-
D1SV.P
-
PP -
DP
-
B
-
PR
-
PH-N
-
zo
BOD
-
0 2
NH4 NO 2 NO 3 CL
CM
-
d i s s o l v e d o r g a n i c and i n o r g a n i c phosphorus sum of d i s s o l v e d o r g a n i c and i n o r g a n i c phosphorus sum of p a r t i c u l a t e phosphorus
d e t r i t e phosphorus b a c t e r i a l phosphorus protozoan phosphorus phytoplankton phosphorus zooplankton phosphorus biochemical oxygen demand oxygen
o r g a n i c n i t r o g e n ammonium n i t r o g e n n i t r i t e n i t r o g e n n i t r a t e n i t r o g e n
l a b i l e carbonous o r g a n i c m a t t e r o r g a n i c m a t t e r transformed by b a c t e r i a
R e c e n t e x p e r i m e n t a l e v i d e n c e h a s e m p h a s i z e d t h e i m p o r t a n c e o f p r o t o z o a a n d z o o p l a n k t o n t y p e s i n t h e t r a n s f o r m a t i o n o f o r g a n i c p h o s p h o r u s . I t was a l s o r e p o r t e d t h a t t h e b a c t e r i a l u p t a k e o f i n o r g a n i c p h o s p h o r u s may i n c r e a s e t h e b a c t e r i a l c o n s u m p t i o n o f o r g a n i c p h o s p h o r u s u n d e r c e r t a i n c o n d i t i o n s , a n d t h a t t h e p r e s e n c e o f many p r e d a t o r s i n p r o p o r t i o n t o b a c t e r i a c a n g r e a t l y a c c e l e r a t e t h e b a c t e r i a l t r a n s f o r m a t i o n o f o r g a n i c p h o s p h o r u s .
1 0 . How c a n a l g a l s u c c e s s i o n b e r e p r e s e n t e d i n t h e m o d e l ? A s b l u e - g r e e n a l g a l b l o o m s a r e a n i m p o r t a n t p r o b l e m , how c o u l d we a t l e a s t d i s t i n g u i s h b e t w e e n " o t h e r a l g a e f r and b l u e - g r e e n a l g a e ?
R e p o r t e d by V.J. B i e r m a n , Jr.
W h e t h e r o r n o t a l g a l s u c c e s s i o n s h o u l d b e r e p r e s e n t e d i n a model d e p e n d s upon t h e p a r t i c u l a r c i r c u m s t a n c e s o f t h e s y s t e m b e i n g c o n s i d e r e d . I n Lake B a l a t o n , f o r e x a m p l e , it was r e p o r t e d t h a t i n t h e summer n o n g r a z e d P y r r h o p h y t a a r e becoming p r e d o m i n a n t o v e r o t h e r g r a z e d s p e c i e s , a n d t h a t a c c u r a t e r e s u l t s c a n n o t b e o b t a i n e d f o r z o o p l a n k t o n c o n c e n t r a t i o n s b y u s i n g o n l y a s i n g l e a l g a l g r o u p i n t h e model. I t i s s u g g e s t e d t h a t a t l e a s t f i v e p h y t o p l a n k t o n t y p e s s h o u l d b e i n c l u d e d i n t h e Lake B a l a t o n model:
B a c i l l a r i o p h y c e 3 ~ ; P y r r h o p h y t a , C y a n o p h y t a , C h l o r o p h y t a , a n d o t h e r s .
A n o t h e r a s p e c t o f a l g a l s u c c e s s i o n was d i s c u s s e d , a l t h o u g h i t h a s n o d i r e c t r e l a t i o n s h i p t o a l g a l p r o d u c t i o n r a t e s . I n Lake B a l a t o n , a s u b s t a n t i a l i n c r e a s e i n b l u e - g r e e n a l g a e f r o m t h e s e d i m e n t l a y e r , w h e r e t h e y grow i n l a r g e q u a n t i t i e s , was r e p o r t e d The o p i n i o n was e x p r e s s e d t h a t e c o l o g i c a l m o d e l s w i l l b e u n a b l e t o d e s c r i b e t h i s phenomenon a d e q u a t e l y .
I n a n a t t e m p t t o d e s c r i b e t h e buoyancy phenomenon i n a n o t h e r l a k e , i t was r e p o r t e d t h a t s e t t l i n g v e l o c i t i e s o f 1 m/day t o 20 m/day were r e q u i r e d i n o r d e r f o r them t o c o r r e s p o n d t o t h e d a t a . I n t h i s c a s e t h e t o t a l b l u e - g r e e n b i o m a s s i n t h e f i r s t 2 c e n t i m e t e r s o f s e d i m e n t e d m a t e r i a l was a p p r o x i m a t e l y t h e same a s t h e t o t a l b l u e - g r e e n b i o m a s s i n t h e w a t e r column.
T h e r e was a s u g g e s t i o n t h a t , i n g e n e r a l , v a r i a b l e s f o r a l g a l s u c c e s s i o n s h o u l d b e i n c l u d e d i n t h e model when
- -
S i l i c a i s l i m i t i n g - - t h i s w i l l c a u s e a s u c c e s s i o n i n s p e c i e s from d i a t o m s t o nondiatoms- -
T h e r e i s a s u b s t a n t i a l b l u e - g r e e n bloom--these s p e c i e s have d i f f e r e n t c h a r a c t e r i s t i c s from o t h e r t y p e s--
F i x a t i o n o f n i t r o g e n i s shown t o t a k e p l a c e - - t h i s f r e - q u e n t l y o c c u r s i n l a k e s , where t h e p h o s p h o r u s / n i t r o g e n r a t i o i s r e l a t i v e l y lowC r i t e r i a f o r s e l e c t i n g a l g a l s p e c i e s w i t h f u n c t i o n a l c h a r a c - t e r i s t i c s b e s t s u i t e d t o a g i v e n s e t o f c i r c u m s t a n c e s were p r e - s e n t e d u s i n g a s e l f - o p t i m i z i n g ( s e l f - o r g a n i z i n g ) p r i n c i p l e w i t h m a x i m i z a t i o n o f a s p e c i f i e d g o a l f u n c t i o n f o r t h e a l g a e . F o r c o m p l e t e i n f o r m a t i o n s e e Radtke and ~ t r a g k r a b a (1 977)
.
The t e m p e r a t u r e p r e f e r e n c e s o f b l u e - g r e e n a l g a e were d i s - c u s s e d . B l u e - g r e e n s a r e u s u a l l y o b s e r v e d t o be dominant when t h e w a t e r t e m p e r a t u r e e x c e e d s 2 0 O C . However, i t was p o i n t e d o u t t h a t t h e r e a r e c e r t a i n b l u e - g r e e n s p e c i e s , f o r example, O s c i Z Z a t o r i a , t h a t grow w e l l a t l o w e r t e m p e r a t u r e s .
I t was p o i n t e d o u t t h a t t h e m i c r o c l i m a t e a r o u n d b l u e - g r e e n a l g a e may l e a d t o c e r t a i n f u n c t i o n a l d i f f e r e n c e s a s compared t o o t h e r t y p e s o f a l g a e . Blue-greens a r e known t o m a i n t a i n a c l o s e r e l a t i o n s h i p w i t h s y m b i o t i c b a c t e r i a . T h i s c h a r a c t e r i s t i c may b e r e s p o n s i b l e f o r i n f l u e n c i n g t h e pH v a l u e and u p t a k e k i n e t i c s f o r p h o s p h o r u s a n d c a r b o n d i o x i d e .
R e f e r e n c e was made t o r e s u l t s a c h i e v e d by S h a p i r o , which i n d i c a t e t h a t b l u e - g r e e n s a r e more e f f i c i e n t t h a n o t h e r s p e c i e s f o r c a r b o n d i o x i d e u p t a k e . T h i s c o n c l u s i o n was c h a l l e n g e d b e c a u s e t h e e x p e r i m e n t s p e r f o r m e d d i d n o t m e a s u r e i n d e p e n d e n t l y t h e e f f e c t o f t h e c h a n g e i n pH on t h e c a r b o n and t h e p h o s p h o r u s - u p t a k e k i n e t - i c . The d i s t r i b u t i o n o f t h e d i s s o l v e d forms o f b o t h n u t r i e n t s c h a n g e s a s a f u n c t i o n o f pH.
T h e r e was d i s c u s s i o n o f t h e p o i n t t h a t commonly a c c e p t e d n o t i o n s o f b l u e - g r e e n s e t t l i n g a n d t h e i r freedom from g r a z i n g p r e s s u r e s may n o t be c o r r e c t i n a l l c a s e s . A p p a r e n t s e t t l i n g v e l o c i t i e s f o r b l u e - g r e e n a l g a e may n o t b e s l o w e r t h a n s e t t l i n g v e l o c i t i e s f o r o t h e r s p e c i e s , b u t may b e more r a p i d d u e t o clumping and c o l o n y f o r m a t i o n . R e c e n t e x p e r i m e n t a l work by McNaught on Lake Huron h a s i n d i c a t e d t h a t b l u e - g r e e n s p e c i e s may a c t u a l l y b e
p r e f e r r e d by t h e z o o p l a n k t o n when compared t o c e r t a i n non-blue- g r e e n s p e c i e s . I n t h e s e c a s e s it i s n o t c l e a r w h e t h e r t h e zoo- p l a n k t o n a s s i m i l a t e t h e b l u e - g r e e n s o r m e r e l y i n g e s t them.
L o c a l b l u e - g r e e n a l g a e p r o b l e m s a r e n o t p r i m a r i l y c a u s e d by t h e i r r a p i d mass g r o w t h , b u t r a t h e r by t h e i r b u o y a n t r i s i n g t o t h e s u r f a c e , where t h e y form c l u m p s . Under t h e s e c i r c u m s t a n c e s t h e well-known d i s a d v a n t a g e o f b i o m a s s d e c a y t h a t i s h i g h l y con- c e n t r a t e d i n a r e l a t i v e l y s m a l l p a r t o f t h e l a k e w i l l a p p e a r . T h i s phenomenon i s v e r y d i f f i c u l t t o i n c l u d e i n t h e model.
1 1 . D o w e n e e d t o i n c l u d e a n a e r o b i c c o n d i t i o n s , d e n i t r i f i c a t i o n , a n d n i t r o g e n f i x a t i o n in t h e model, a n d , if so, how?
R e p o r t e d by G. v a n S t r a t e n
One a p p r o a c h i n which t h e e f f e c t s o f n i t r o g e n f i x a t i o n upon t h e n i t r o g e n b u d g e t c a n b e t a k e n i n t o a c c o u n t i s t o s e t t h e r a t e o f n i t r o g e n f i x a t i o n p r o p o r t i o n a l t o t h e n i t r o g e n d e f i c i e n c y , c a l c u l a t e d from t h e d i s c r e p a n c y between t h e s o l u b l e n i t r o g e n a n d p h o s p h o r u s r a t i o i n t h e w a t e r and t h e p h o s p h o r u s / n i t r o g e n u p t a k e r a t e . T h e r e seems t o b e no s h a r p t h r e s h o l d c o n c e n t r a t i o n f o r n i t r o g e n f i x a t i o n - - s o m e 300 pg n i t r o g e n / l i t e r o f s o l u b l e n i t r o g e n h a s b e e n m e n t i o n e d a s a s u i t a b l e f i g u r e . A s i m p l e s o l u t i o n i s t o s e t t h e f i x a t i o n r a t e a t z e r o f o r 300 pg n i t r o g e n / l i t e r and t o a c c o u n t f o r a l i n e a r i n c r e a s e i f s o l u b l e n i t r o g e n d r o p s t o z e r o . T h i s i s a more e l a b o r a t e c a s e o f t h e s i m p l e a p p r o a c h whereby n i t r o g e n i s n o t a l l o w e d t o become l i m i t i n g t o t h e n i t r o g e n - f i x i n g b l u e - g r e e n a l g a e ; o n e m e r e l y t r a c e s t h e c h a n g e s o f n i t r o g e n d u r i n g t h e i r g r o w t h . To p r e v e n t p r o b l e m s r e g a r d i n g t h e r a t i o o f n i t r o g e n - f i x i n g t o n o n - n i t r o g e n - f i x i n g a l g a e , t h e i n t r o d u c t i o n o f a s e p a - r a t e s t a t e v a r i a b l e f o r n i t r o g e n - f i x i n g a l g a e m i g h t be e n v i s a g e d .
T h e r e was g e n e r a l a g r e e m e n t a b o u t t h e o c c u r r e n c e o f d e n i t r i - f i c a t i o n i n t h e s e d i m e n t . The t h e o r e t i c a l p o s s i b i l i t y o f d e n i t r i - f i c a t i o n i n t h e oxygen d e p l e t e d c o r e o f a l g a e clumps d o e s n o t seem t o b e i m p o r t a n t i n p r a c t i c e . For d e n i t r i f i c a t i o n t o o c c u r i t d o e s n o t seem t o b e o f g r e a t s i g n i f i c a n c e t h a t t h e s e d i m e n t i s e n t i r e l y a n a e r o b i c , b e c a u s e t h e r e w i l l a l w a y s b e n i t r a t e p r e s e n t i n t h e s e d i m e n t i n t h e a n a e r o b i c p o r t i o n s , s i n c e n i t r a t e p e n e t r a t e s much
d e e p e r t h a n o x y g e n . A s i m p l e f i r s t - o r d e r r e a c t i o n h a s b e e n a p p l i e d a s a r e a s o n a b l e a p p r o x i m a t i o n o f d e n i t r i f i c a t i o n , a l t h o u g h t h e r e s u l t s o f a n a l y s i s o f t h e s i m u l t a n e o u s d i f f u s i o n a n d r e a c t i o n s y s t e m would s u g g e s t a s q u a r e r o o t d e p e n d e n c e ( a h a l f - o r d e r d e p e n - d e n c e ) . Of c o u r s e , a more d e t a i l e d m o d e l would r e q u i r e t h e i n c o r - p o r a t i o n o f d e n i t r i f y i n g b a c t e r i a .
1 2 . How d o we s e l e c t t h e n e c e s s a r y number o f s t a t e v a r i a b l e s f o r s o l v i n g a s p e c i f i c p r o b l e m ? A g r e a t e r number o f s t a t e v a r i - a b l e s i n v o l v e s t h e i n t r o d u c t i o n o f more p a r a m e t e r s , and more
m e a s u r e m e n t s m u s t a l s o be c a r r i e d o u t , w h i l e f e w e r s t a t e v a r i a b l e s may n o t d e s c r i b e t h e s t r u c t u r e o f t h e s y s t e m i n s u f f i c i e n t d e t a i l . How d o we f i n d t h e p o i n t o f b a l a n c e ? What i s t h e r o l e o f c h e m i c a l d a t a ?
R e p o r t e d by M. ~ t r a g k r a b a
T h r e e m e t h o d s w e r e s u g g e s t e d f o r s e l e c t i n g t h e number o f s t a t e v a r i a b l e s t o b e i n c l u d e d i n t h e m o d e l . The f i r s t i s t o u s e t h e c r i t e r i o n o f e c o l o g i c a l b u f f e r c a p a c i t y B w h i c h i s e x p r e s s e d a s t h e r a t i o b e t w e e n c h a n g e i n l o a d i n g a n d c h a n g e i n t h e s t a t e v a r i a b l e s o f i n t e r e s t - - e . g . , B = ( A l o a d i n g ) / ( A P S ) , w h e r e PS i s t h e s t a t e v a r i a b l e r e p r e s e n t i n g s o l u b l e p h o s p h o r u s . F o r f u r - t h e r d e t a i l s , see J b r g e n s e n a n d Meyer ( 1 9 7 7 ) . I t was s t a t e d t h a t
c a n n o t b e u s e d f o r c o m p a r i n g s e v e r a l m o d e l s . I t i s n o t i c e a b l e t h a t B i s t i m e d e p e n d e n t , i f s u c h e x t e r n a l f a c t o r s a s t e m p e r a t u r e a n d i r r a d i a n c e a r e f u n c t i o n s o f t i m e .
The s e c o n d m e t h o d i s o n e t o d e c i d e w h i c h d e g r e e o f model c o m p l e x i t y i s s u f f i c i e n t f o r a s p e c i f i c p u r p o s e . The v a r i a n c e o f t h e p r o p e r t y t h a t t h e model i s i n t e n d e d t o p r e d i c t i s a f f e c t e d by t h e number o f s t a t e v a r i a b l e s o r p a r a m e t e r s . W e a s s u m e t h a t t h e p u r p o s e o f t h e model i s t o p r e d i c t t h e c o n s e q u e n c e s o f some c h a n g e s t o t h e s y s t e m u n d e r s t u d y , s u c h a s i n c r e a s e d l o a d i n g . W e a l s o a s s u m e t h a t t h e c h a n g e c a n b e q u a n t i f i e d by some n u m e r i c a l q u a n t i t y P ( s u c h a s t h e maximum c o n c e n t r a t i o n o f p h y t o p l a n k t o n ) . A m o d e l b a s e d o n N 1 p a r a m e t e r s , a w i l l y i e l d a n e s t i m a t e
P ( N ~ )
N 1 '
of P , a n d t h i s e s t i m a t e w i l l h a v e a s a m p l i n g d i s t r i b u t i o n , b e c a u s e i t s p a r a m e t e r s a r e c a l c u l a t e d f r o m o b s e r v e d d a t a t h a t c a n be
regarded as random variables. Similarly, a more complex model with N2 parameters ci (N > N 1 ) will yield a second estimate
N2 A 2
3
( N ~ ) ofP;
the closer P (N1 ) is to P , the better the model. It is suggested that the root mean square error could be taken as a measure of the model's "goodness-of-fit." However, P is never known, therefore some less satisfactory alternative has to be used, such as var16 (Nil1.
Now var{G (Ni)1
is a function of the sampling variances--i.e.,This quantity will have more or fewer terms depending upon whether the model is complex (N1 large) or simple (Ni small). We could
A
therefore plot var{P(Ni)l as ordinate against Ni as abscissa, and choose that value of Nil beyond which an increase in the number
A
of parameters gives little or no reduction in var{p(Ni)
1.
This approach could be adapted to include consideration of the greater cost associated with more complex models; if the cost were taken as a linear function of Nil and A and B are constants, the number of parameters would show thatCost = A
+
BN iand then the picture given in Figure 2 would be obtained. The model with N* parameters would then be adequate for the specified purpose.
The third method has not yet been tested in practice. It involves the development of some statistical indices similar to the indices of diversity, where, instead of the number of species, the number of variables would be used.
Generally it was felt that we need more systems analysis methods, in order to choose the correct level of complexity, and to validate the more complicated models. Other aspects of vali- dation were raised, particularly the impossibility in most
F i g u r e 2. Curve: showing t h e a c c u r a c y , v a r { P ( N i )
1,
and c o s t a s s o c i - a t e d w i t h h a v i n g a model w i t h N i p a r a m e t e r s .i n s t a n c e s o f v a l i d a t i n g t h e model u n d e r d i f f e r e n t c o n d i t i o n s o f n u t r i e n t l o a d i n g . Even when l o a d i n g a r e c h a n g e d , t h e r e s p o n s e i n most c a s e s w i l l b e d e l a y e d ; t h u s , i t w i l l b e n e c e s s a r y f o r s e v e r a l y e a r s t o e l a p s e b e f o r e a n a c c u r a t e v a l i d a t i o n c a n b e u n d e r t a k e n . I t was s u g g e s t e d t h a t a v a l i d a t i o n o f t h e same model s h o u l d b e a p p l i e d t o a number o f l a k e s w i t h d i f f e r e n t l o a d i n g s . F i n a l l y , i t may b e n o t e d t h a t t h e l e v e l o f model e r r o r i n c r e a s e s w i t h an i n c r e a s e i n t h e number o f p a r a m e t e r s .
13. How r e l i a b l e a r e p r e s e n t - d a y e c o l o g i c a l m o d e l s ? To w h a t e x t e n t i s i t p o s s i b l e t o p r e d i c t t h e r e s p o n s e o f t h e l a k e t o c h a n g e d l o a d i n g ?
R e p o r t e d by P . M a u e r s b e r g e r and K . Bauer
From t h e m a t h e m a t i c a l p o i n t o f view t h e e q u a t i o n s c h a r a c t e r - i z i n g a m i c r o s c o p i c , d e t e r m i n i s t i c , w a t e r q u a l i t y model form a s y s t e m o f n o n l i n e a r d i f f e r e n t i a l e q u a t i o n s w i t h b o u n d a r y con- d i t i o n s and i n i t i a l v a l u e s . I t i s d i f f i c u l t t o i n v e s t i g a t e t h e e x i s t e n c e a n d u n i q u e n e s s o f t h e s o l u t i o n t o t h e s e e q u a t i o n s . From t h e thermodynamic p o i n t o f view t h e a q u a t i c e c o s y s t e m i s a n o n l i n e a r open s y s t e m , e x c h a n g i n g e n e r g y and m a t t e r w i t h t h e e n v i r o n m e n t , which i s f a r from thermodynamic e q u i l i b r i u m . I n c o m p l e t i n g t h i s s y s t e m o f b a s i c e q u a t i o n s by a d d i n g e n t r o p y , i t becomes p o s s i b l e t o a p p l y t h e methods a n d r e s u l t s o f t h e modern t h e o r y o f thermodynamics o f i r r e v e r s i b l e p r o c e s s e s ( P r i g o g i n e ,
1972) t o a q u a t i c e c o s y s t e m s . T h i s t h e o r y o f f e r s l o c a l a n d g l o b a l
evolution and stability criteria. The mutual effect of entropy- producing and entropy-reducing processes inside the water body and across its boundaries regulates the structure, state, and further development of the aquatic ecosystem. Since the nonlinear basic equations are shown, in general, to have more than one solu- tion when the system is sufficiently distant from thermodynamic equilibrium, fluctuations (generated by the system itself or excited by external factors) play an important role during the transition of the ecosystem to a new structure. The succession of structures characterizes the anthropogenically influenced pro- cesses of self-adaptation and self-organization of the ecosystem.
This theory has not yet been fully elaborated. In particular, the regulating mechanisms of living subsystems should be included;
thermodynamic and cybernetic considerations must be combined, and stochastic elements should be incorporated into the model. Despite its incompleteness, such a theory may provide precisely the "com- prehensive" (or "condensed") approach to water quality modeling that was called for in the introduction to this workshop.
Many problems relating to the predictability of the model's responses to changed loading remain open to discussion. For example, is the influence of microcontaminants, molybdenum oxide, glycine, and the like taken into account in such a way that the model reacts correctly to c:hanges in the concentrations of these
substances.
1 4 . I s i t p o s s i b l e t o d e v e l o p m o d e l s f o r p r e d i c t i n g t h e r a t e o f e u t r o p h i c a t i o n ? S h o u l d s i m p l e o r c o m p l e x m o d e l s b e u s e d ? what i s t h e p o t e n t i a l i t y and what a r e t h e l i m i t a t i o n s o f t h e m o d e l s ? Are t h e a n a l y t i c a l e x p r e s s i o n s o f t h e r e l a t i o n s h i p b e t w e e n p h y t o - p l a n k t o n b i o m a s s and t o t a l l o a d i n g o f n u t r i e n t s , a v e r a g e d e p t h , r e t e n t i o n t i m e o f w a t e r , and t h e l i k e v a l i d ( V o l l e n w e i d e r i n d e x ) ?
Reported by V.A. Vavilin
If a modification of Vollenweider's approach is used, then
where B is the phytoplankton concentration, X is the limiting nutrient concentration, T = V/q is the mean retention time (V is the volume of the water body, q is the flow), y is a stoichiometric coefficient, p(X,t,I) is the phytoplankton growth rate as a func- tion of the limiting nutrient concentration X, (t) is temperature, I is the light intensity, and Xo is the nutrient concentration of the in£ luent.
Let us now assume that
where
f (I) = I
1 1 ~
I'
Imand where Im is a saturation constant. Then
in which Kx is a half-saturation coefficient.
The intensity of light at depth h is
where I is the light intensity at the surface, no is the light-
0
absorption coefficient for water, n is the specific extinction- absorption coefficient for phytoplankton. Thus, if light inten- sity is a limiting factor at depth
then
-
(no+nB) HIm
<
.I<
Ime Iwhere H is the maximum depth.
The mean v a l u e i s g i v e n by
a n d , i n s t e a d o f t h e i n f l u e n t c o n c e n t r a t i o n o f l i m i t i n g n u t r i e n t Xo, l e t u s now c o n s i d e r t h e mean n u t r i e n t l o a d i n g X E
i n w h i c h S i s a s u r f a c e o f w a t e r b o d y .
Under a s t e a d y - s t a t e c o n d i t i o n t h e s e e q u a t i o n s a r e t r a n s - formed i n t o
I n t h e l i n e a r c a s e Kx > > X. I f
t h e n
w h e r e
From the Equation
(18)it is easy to obtain
We can distinguish between
B < B+
--oligotrophic state
B+ < B < B++ --mesotrophic state
B > B++
--eutrophic state
From this Figure
3is obtained, where the parameters
y,q/s, no/n are constants in a specified case.
In a more general case when Equation
( 1 3 )is valid, the following expression can be obtained.
Equation
( 2 1 )is plotted in Figure
4.It is possible to consider some modifications of Equation
(7). A sgiven, the model permits an accurate estimation of the trophic state, when the limiting-nutrient loading is changed.
The classification of lakes, according to deduction from the Vollenweider-type diagram, is not suitable in some instances.
Figure
3.The distinction between oligotrophic, mesotrophic, and eutrophic states on
the basis of Equation
( 2 0 ) .Figure 4. The distinction between oligotrophic, nesotrophic, and eutrophic states on the basis of Equation ( 2 1 ) .
Dillon improved this approach, by considering the dilution rate as an important parameter.
The approach presented above depends upon retention time, depth and intensity of light, maximum growth rate, etc. The important question is whether the steady-state approach is valid both for the model and for the real lake system. In systems analysis it is important to establish whether the local stability conditions are indicative of globally stable dynamic behavior.
The validity of the steady-state approach depends primarily upon seasonal variations of nutrient loading.
Vollenweider's approach is attractive because of its sim- plicity--it requires no large-scale experimental work. However, from a decision-making point of view, it seems necessary to con- struct and investigate dynamic models.
1 5 . What p a r a m e t e r s and p r o c e s s e s s h o u l d be c o n s i d e r e d f o r t h e l a k e s u b j e c t t o a c i d i c d e p o s i t i o n ?
Reported by M.W. Lorenzen
A survey of lake susceptibility to acid precipitation would be useful.
It was noted that literature from Norway and Sweden has reported on stddies in those countries; and the Workshop offered no final conclusion about how to solve this problem.
1 6 . A s u g g e s t i o n f o r a n I I A S A p u b l i c a t i o n : s h o u l d I I A S A p u b l i s h a l i s t o f p a r a m e t e r s ?
Reported by L.
J.
HajduThe value of model parameters is of great interest for all scientists working in the field of ecological modeling. Many data are to be found in the literature, but a handbook containing the most important parameters, such as half-saturation constants, death, sinking, grazing rates, minimum phosphorus concentrations in algae, would be useful.
Concurrent with the development of the field, revision of these parameters values must take place. It was recommended that a list of parameters be completed according to standard units
(SI), with the necessary conversion tables included. It might also be of interest to standardize techniques of parameter mea- surement--e.g., for the phosphorus half-saturation constant, since it is not a constant parameter but changes according to ecological and hydrological factors. The methodology of parameter measurement may appear to be of marginal interest to IIASA, but undoubtedly the reality of a model is to a great extent dependent upon the reliability of the basic parameters.
Modern limnology textbooks reflect this attitude to modeling, but they may be of limited value to the practical model builder, since they usually contain few suitable model parameters. The general validity of these parameters is not fully understood, but if a collection of widely distributed literature data were available, it would make possible the study of the generality of the parameter values suggested by several authors. It would also be useful to include a recommended literature list and the ad- dresses of authors and contributors in the handbook suggested above.
It was announced that such a handbook was being prepared in Denmark and would be ready for publication in the autumn of 1 9 7 8 . The data would be available on tapes. Approximately 5 0 inter- national journals and 5 0 0 books have been reviewed, and the hand- book will probably cover 7 5 percent or more of the total relevant literature. Parameter values only are compiled without critical
